f(x)=sin(2x+π/3)=f(0)在(0,2π)成立的x的集合为______答案为{π,7π/6,π/6}

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f(x)=sin(2x+π/3)=f(0)在(0,2π)成立的x的集合为______答案为{π,7π/6,π/6}
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f(x)=sin(2x+π/3)=f(0)在(0,2π)成立的x的集合为______答案为{π,7π/6,π/6}
f(x)=sin(2x+π/3)=f(0)在(0,2π)成立的x的集合为______
答案为{π,7π/6,π/6}

f(x)=sin(2x+π/3)=f(0)在(0,2π)成立的x的集合为______答案为{π,7π/6,π/6}
f(0)=sin(0+π/3)=√3/2
sin(2x+π/3)=√3/2
∵x∈(0,2π)
∴2x+π/3∈(π/3,13π/3)
于是
2x+π/3=2π/3或7π/3或8π/3
2x=π/3或2π或7π/3
x=π/6或π或7π/6
即x的集合为{π/6,π,7π/6}